I have a total of Rs. 1,000. Item A costs Rs. 110, item B costs Rs. 90, item C costs Rs. 70, item D costs Rs. 40 and item E costs Rs. 45. For every item D that I purchase, I must also buy two of item B. For every item A, I must buy one of item C. For every item E, I must also buy two of item D and one of item B. For every item purchased I earn 1,000 points and for every rupee not spent I earn a penalty of 1,500 points. My objective is to maximise the points I earn. What is the number of items that I must purchase to maximise my points?

According to given condition we find average costs for products bought.
If D is bought then - D +2*B . So we spend 40+180 =220 Rs for 3000 points. Hence, cost per 1000 points is 73.33
If A is bought then - A+C . So we spend 110 + 70 = 180 for 2000 points. Hence, cost per 1000 points is 90
If E is bought then - E+2*D+4*B+B . So we spend 45 + 80 + 360 + 90 = 575 for 8000 points. Hence, cost per 1000 points is 71.875.

If B is bought then I spend Rs 90 per 1000 points.

If C is bought then I spend Rs 70 per 1000 points.

To maximise points we need to select the item that costs the least per 1000 points. Hence, C costs the least per 1000 points. Hence, we should buy as many C items as possible.
Maximum C that can be bought is [1000/70] = 14 items and Rs 20 would be left over. However, the unspent money would attract a penalty of 30000 points. Hence, instead of buying 14 C items, we should buy 13 C items and 1 B item so that total money spent is 1000.